Finite Group Databasebeta

← C31×#14520 #21471279

Subgroups — C31×#14520 #21471279

Order 7936.

2182 conjugacy classes of subgroups.

The subgroup lattice has 1316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#392C211yesmaximal, characteristic
2C2×C31×#390C211yesmaximal, characteristic, complemented
3C2×C31×#388C211yesmaximal, characteristic, complemented
4C2×C31×#386C211yesmaximal, characteristic, complemented
5C2×C31×#386C211yesmaximal, characteristic, complemented
6C31×#1442C211yesmaximal, characteristic, complemented
7C31×#1440C211yesmaximal, characteristic, complemented
8C31×#1438C211yesmaximal, characteristic, complemented
9C31×#1438C211yesmaximal, characteristic, complemented
10C31×#1438C211yesmaximal, characteristic, complemented
11C31×#1437C211yesmaximal, characteristic, complemented
12C31×#1437C211yesmaximal, characteristic, complemented
13C31×#1437C211yesmaximal, characteristic, complemented
14C31×#1434C211yesmaximal, characteristic, complemented
15C31×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C31C2211yescharacteristic
17C23×D4×C31C2211yescharacteristic
18C23×D4×C31C2211yescharacteristic
19C24×C4×C31C2211yescharacteristic
20C22×C4⋊C4×C31C2211yescharacteristic
21C22×C22⋊C4×C31C2211yescharacteristic
22C22×C22⋊C4×C31C2211yescharacteristic
23C22×C22⋊C4×C31C2211yescharacteristic
24C22×C22⋊C4×C31C2211yescharacteristic
25C22×C22⋊C4×C31C2211yescharacteristic
26C22×C22⋊C4×C31C2211yescharacteristic
27C22×C22⋊C4×C31C2211yescharacteristic
28C22×C22⋊C4×C31C2211yescharacteristic
29C22×C22⋊C4×C31C2211yescharacteristic
30C22×C22⋊C4×C31C2211yescharacteristic
31C22×C22⋊C4×C31C2211yescharacteristic
32C22×C22⋊C4×C31C2211yescharacteristic
33C22×C22⋊C4×C31C2211yescharacteristic
34C22×C22⋊C4×C31C2211yescharacteristic
35C22×C42×C31C2211yescharacteristic
36C22×C42×C31C2211yescharacteristic
37C31×#392C418yescomplemented
38C31×#390—24no—
39C31×#388—24no—
40C31×#386—24no—
41C31×#386—24no—
42C2×C31×#95C2211yescharacteristic
43C2×C31×#95C2211yescharacteristic
44C2×C31×#95C2211yescharacteristic
45C2×C31×#95C2211yescharacteristic
46C2×C31×#95C2211yescharacteristic
47C2×C31×#95C2211yescharacteristic
48C2×C31×#95C2211yescharacteristic
49C2×C31×#95C2211yescharacteristic
50C2×C31×#95C2211yescharacteristic
51C2×C31×#95C2211yescharacteristic
52C2×C31×#95C2211yescharacteristic
53C2×C31×#95C2211yescharacteristic
54C2×C31×#95C2211yescharacteristic
55C2×C31×#95C2211yescharacteristic
56C25×C31C2311yescharacteristic
57C25×C31C2311yescharacteristic
58C25×C31C2311yescharacteristic
59C22×D4×C31—22no—
60C22×D4×C31—22no—
61C22×D4×C31—22no—
62C22×D4×C31—22no—
63C22×D4×C31—22no—
64C22×D4×C31—22no—
65C22×D4×C31—41no—
66C22×D4×C31—41no—
67C22×D4×C31—41no—
68C22×D4×C31—41no—
69C22×D4×C31—41no—
70C22×D4×C31—41no—
71C22×D4×C31—41no—
72C22×D4×C31—41no—
73C22×D4×C31—41no—
74C22×D4×C31—41no—
75C22×D4×C31—41no—
76C22×D4×C31—41no—
77C22×D4×C31C2×C414yes—
78C22×D4×C31C2×C414yes—
79C22×D4×C31C2×C414yescomplemented
80C23×C4×C31—22no—
81C23×C4×C31—22no—
82C23×C4×C31—22no—
83C23×C4×C31—41no—
84C23×C4×C31—41no—
85C23×C4×C31—41no—
86C23×C4×C31—41no—
87C23×C4×C31C2311yescharacteristic
88C23×C4×C31C2311yescharacteristic
89C23×C4×C31C2311yescharacteristic
90C23×C4×C31C2311yescharacteristic
91C23×C4×C31C2311yescharacteristic
92C23×C4×C31C2311yescharacteristic
93C23×C4×C31C2311yescharacteristic
94C23×C4×C31C2311yescharacteristic
95C23×C4×C31C2311yescharacteristic
96C23×C4×C31C2311yescharacteristic
97C23×C4×C31C2311yescharacteristic
98C23×C4×C31C2311yescharacteristic
99C2×C4⋊C4×C31—22no—
100C2×C4⋊C4×C31—22no—
101C2×C4⋊C4×C31—41no—
102C2×C22⋊C4×C31—22no—
103C2×C22⋊C4×C31—22no—
104C2×C22⋊C4×C31—22no—
105C2×C22⋊C4×C31—22no—
106C2×C22⋊C4×C31—22no—
107C2×C22⋊C4×C31—22no—
108C2×C22⋊C4×C31—22no—
109C2×C22⋊C4×C31—22no—
110C2×C22⋊C4×C31—22no—
111C2×C22⋊C4×C31—22no—
112C2×C22⋊C4×C31—22no—
113C2×C22⋊C4×C31—22no—
114C2×C22⋊C4×C31—22no—
115C2×C22⋊C4×C31—22no—
116C2×C22⋊C4×C31—22no—
117C2×C22⋊C4×C31—22no—
118C2×C22⋊C4×C31—22no—
119C2×C22⋊C4×C31—22no—
120C2×C22⋊C4×C31—41no—
121C2×C22⋊C4×C31—41no—
122C2×C22⋊C4×C31—41no—
123C2×C22⋊C4×C31—41no—
124C2×C22⋊C4×C31—41no—
125C2×C22⋊C4×C31—41no—
126C2×C22⋊C4×C31—41no—
127C2×C22⋊C4×C31—41no—
128C2×C22⋊C4×C31—41no—
129C2×C22⋊C4×C31—41no—
130C2×C22⋊C4×C31—41no—
131C2×C22⋊C4×C31—41no—
132C2×C22⋊C4×C31—41no—
133C2×C22⋊C4×C31—41no—
134C2×C22⋊C4×C31—41no—
135C2×C22⋊C4×C31—41no—
136C2×C22⋊C4×C31—41no—
137C2×C22⋊C4×C31—41no—
138C2×C22⋊C4×C31—41no—
139C2×C22⋊C4×C31—41no—
140C2×C22⋊C4×C31C2×C414yes—
141C2×C22⋊C4×C31C2×C414yescomplemented
142C2×C22⋊C4×C31C2×C414yescomplemented
143C2×C22⋊C4×C31D414yescomplemented
144C2×C42×C31—22no—
145C2×C42×C31—22no—
146C2×C42×C31—22no—
147C2×C42×C31—41no—
148C2×C42×C31—41no—
149C2×C42×C31—41no—
150C31×#95—22no—
151C31×#95—22no—
152C31×#95—22no—
153C31×#95—22no—
154C31×#95—41no—
155C31×#95—41no—
156C31×#95—41no—
157C31×#95—41no—
158C31×#95—41no—
159C31×#95—41no—
160C31×#95—41no—
161C31×#95—41no—
162C31×#95C2×C414yescomplemented
163C31×#95D414yescomplemented
164C24×C31—21no—
165C24×C31—21no—
166C24×C31—21no—
167C24×C31—21no—
168C24×C31—21no—
169C24×C31—21no—
170C24×C31—21no—
171C24×C31—21no—
172C24×C31—21no—
173C24×C31—21no—
174C24×C31—21no—
175C24×C31—21no—
176C24×C31—21no—
177C24×C31—21no—
178C24×C31—21no—
179C24×C31—21no—
180C24×C31—21no—
181C24×C31—21no—
182C24×C31—21no—
183C24×C31—21no—
184C24×C31—21no—
185C24×C31—21no—
186C24×C31—21no—
187C24×C31—21no—
188C24×C31—21no—
189C24×C31—21no—
190C24×C31—21no—
191C24×C31—21no—
192C24×C31—21no—
193C24×C31—21no—
194C24×C31—21no—
195C24×C31—21no—
196C24×C31—21no—
197C24×C31—21no—
198C24×C31—21no—
199C24×C31—21no—
200C24×C31—21no—
201C24×C31—21no—
202C24×C31—21no—
203C24×C31—21no—
204C24×C31C22×C412yes—
205C24×C31C22×C412yes—
206C24×C31C22×C412yes—
207C24×C31C2×D412yes—
208C24×C31#4112yes—
209C24×C31C2411yescharacteristic
210C2×D4×C31—28no—
211C2×D4×C31—28no—
212C2×D4×C31—28no—
213C2×D4×C31—44no—
214C2×D4×C31—44no—
215C2×D4×C31—44no—
216C2×D4×C31—44no—
217C2×D4×C31—44no—
218C2×D4×C31—44no—
219C2×D4×C31—44no—
220C2×D4×C31—44no—
221C2×D4×C31—44no—
222C2×D4×C31—44no—
223C2×D4×C31—44no—
224C2×D4×C31—44no—
225C2×D4×C31—44no—
226C2×D4×C31—44no—
227C2×D4×C31—44no—
228C2×D4×C31—44no—
229C2×D4×C31—44no—
230C2×D4×C31—44no—
231C22×C4×C31—21no—
232C22×C4×C31—21no—
233C22×C4×C31—21no—
234C22×C4×C31—21no—
235C22×C4×C31—21no—
236C22×C4×C31—21no—
237C22×C4×C31—21no—
238C22×C4×C31—21no—
239C22×C4×C31—21no—
240C22×C4×C31—21no—
241C22×C4×C31—21no—
242C22×C4×C31—21no—
243C22×C4×C31—21no—
244C22×C4×C31—21no—
245C22×C4×C31—21no—
246C22×C4×C31—21no—
247C22×C4×C31—21no—
248C22×C4×C31—21no—
249C22×C4×C31—21no—
250C22×C4×C31—21no—
251C22×C4×C31—21no—
252C22×C4×C31—21no—
253C22×C4×C31—21no—
254C22×C4×C31—21no—
255C22×C4×C31—21no—
256C22×C4×C31—21no—
257C22×C4×C31—21no—
258C22×C4×C31—21no—
259C22×C4×C31—21no—
260C22×C4×C31—21no—
261C22×C4×C31—21no—
262C22×C4×C31—21no—
263C22×C4×C31—21no—
264C22×C4×C31—21no—
265C22×C4×C31—21no—
266C22×C4×C31—21no—
267C22×C4×C31—21no—
268C22×C4×C31—21no—
269C22×C4×C31—21no—
270C22×C4×C31—21no—
271C22×C4×C31—21no—
272C22×C4×C31—21no—
273C22×C4×C31—21no—
274C22×C4×C31—21no—
275C22×C4×C31—21no—
276C22×C4×C31—21no—
277C22×C4×C31—21no—
278C22×C4×C31—21no—
279C22×C4×C31—21no—
280C22×C4×C31—21no—
281C22×C4×C31—21no—
282C22×C4×C31—21no—
283C22×C4×C31—21no—
284C22×C4×C31—21no—
285C22×C4×C31—21no—
286C22×C4×C31—21no—
287C22×C4×C31—21no—
288C22×C4×C31—21no—
289C22×C4×C31—21no—
290C22×C4×C31—21no—
291C22×C4×C31—21no—
292C22×C4×C31—21no—
293C22×C4×C31—21no—
294C22×C4×C31—21no—
295C22×C4×C31—21no—
296C22×C4×C31—21no—
297C22×C4×C31—21no—
298C22×C4×C31—21no—
299C22×C4×C31—21no—
300C22×C4×C31—21no—
301C22×C4×C31—21no—
302C22×C4×C31—21no—
303C22×C4×C31—44no—
304C22×C4×C31—44no—
305C22×C4×C31—44no—
306C22×C4×C31—44no—
307C22×C4×C31—44no—
308C22×C4×C31—44no—
309C22×C4×C31—44no—
310C22×C4×C31C22×C412yes—
311C22×C4×C31C22×C412yes—
312C22×C4×C31C22×C412yes—
313C22×C4×C31C22×C412yes—
314C22×C4×C31C2×D412yes—
315C22×C4×C31C2×D412yes—
316C22×C4×C31C2×D412yes—
317C22×C4×C31C2×D412yes—
318C22×C4×C31C2×D412yes—
319C22×C4×C31#4112yes—
320C22×C4×C31#4112yes—
321C22×C4×C31#4112yes—
322C4⋊C4×C31—44no—
323C22⋊C4×C31—28no—
324C22⋊C4×C31—44no—
325C22⋊C4×C31—44no—
326C22⋊C4×C31—44no—
327C22⋊C4×C31—44no—
328C22⋊C4×C31—44no—
329C22⋊C4×C31—44no—
330C22⋊C4×C31—44no—
331C22⋊C4×C31—44no—
332C22⋊C4×C31—44no—
333C22⋊C4×C31—44no—
334C22⋊C4×C31—44no—
335C22⋊C4×C31—44no—
336C22⋊C4×C31—44no—
337C42×C31—44no—
338C42×C31—44no—
339#14520C3111yesmaximal, characteristic, direct product factor, Sylow
340C23×C31—22no—
341C23×C31—22no—
342C23×C31—22no—
343C23×C31—22no—
344C23×C31—22no—
345C23×C31—22no—
346C23×C31—22no—
347C23×C31—22no—
348C23×C31—22no—
349C23×C31—22no—
350C23×C31—22no—
351C23×C31—22no—
352C23×C31—22no—
353C23×C31—22no—
354C23×C31—22no—
355C23×C31—22no—
356C23×C31—22no—
357C23×C31—22no—
358C23×C31—22no—
359C23×C31—22no—
360C23×C31—22no—
361C23×C31—22no—
362C23×C31—22no—
363C23×C31—22no—
364C23×C31—22no—
365C23×C31—22no—
366C23×C31—22no—
367C23×C31—22no—
368C23×C31—22no—
369C23×C31—22no—
370C23×C31—22no—
371C23×C31—22no—
372C23×C31—41no—
373C23×C31—41no—
374C23×C31—41no—
375C23×C31—41no—
376C23×C31—41no—
377C23×C31—41no—
378C23×C31—41no—
379C23×C31—41no—
380C23×C31—41no—
381C23×C31—41no—
382C23×C31—41no—
383C23×C31—41no—
384C23×C31—41no—
385C23×C31—41no—
386C23×C31—41no—
387C23×C31—41no—
388C23×C31—41no—
389C23×C31—41no—
390C23×C31—41no—
391C23×C31—41no—
392C23×C31—41no—
393C23×C31—41no—
394C23×C31—41no—
395C23×C31—41no—
396C23×C31—41no—
397C23×C31—41no—
398C23×C31—41no—
399C23×C31—41no—
400C23×C31—41no—
401C23×C31—41no—
402C23×C31—41no—
403C23×C31—41no—
404C23×C31—41no—
405C23×C31—41no—
406C23×C31—41no—
407C23×C31—41no—
408C23×C31—41no—
409C23×C31—41no—
410C23×C31—41no—
411C23×C31—41no—
412C23×C31—41no—
413C23×C31—41no—
414C23×C31—41no—
415C23×C31—41no—
416C23×C31—41no—
417C23×C31—41no—
418C23×C31—41no—
419C23×C31—41no—
420C23×C31—41no—
421C23×C31—41no—
422C23×C31—41no—
423C23×C31—41no—
424C23×C31—41no—
425C23×C31—41no—
426C23×C31—41no—
427C23×C31—41no—
428C23×C31—41no—
429C23×C31—41no—
430C23×C31—41no—
431C23×C31—41no—
432C23×C31—41no—
433C23×C31—41no—
434C23×C31—41no—
435C23×C31—41no—
436C23×C31—41no—
437C23×C31—41no—
438C23×C31—41no—
439C23×C31—41no—
440C23×C31—41no—
441C23×C31—41no—
442C23×C31—41no—
443C23×C31—41no—
444C23×C31C4×D414yes—
445C23×C31C23×C411yescharacteristic
446C23×C31C22×D411yescharacteristic
447C23×C31C22×D411yescharacteristic
448C23×C31C2×#4111yescharacteristic
449C23×C31C2×#4111yescharacteristic
450C23×C31C2×#4111yescharacteristic
451C23×C31C2×#4111yescharacteristic
452C23×C31H(5,𝔽2)11yescharacteristic
453C23×C31H(5,𝔽2)11yescharacteristic
454C23×C31H(5,𝔽2)11yescharacteristic
455C23×C31H(5,𝔽2)11yescharacteristic
456C23×C31H(5,𝔽2)11yescharacteristic
457C23×C31H(5,𝔽2)11yescharacteristic
458C23×C31H(5,𝔽2)11yescharacteristic
459C23×C31H(5,𝔽2)11yescharacteristic
460D4×C31—416no—
461D4×C31—416no—
462D4×C31—416no—
463C2×C4×C31—22no—
464C2×C4×C31—22no—
465C2×C4×C31—22no—
466C2×C4×C31—22no—
467C2×C4×C31—22no—
468C2×C4×C31—22no—
469C2×C4×C31—22no—
470C2×C4×C31—22no—
471C2×C4×C31—22no—
472C2×C4×C31—22no—
473C2×C4×C31—22no—
474C2×C4×C31—22no—
475C2×C4×C31—22no—
476C2×C4×C31—22no—
477C2×C4×C31—22no—
478C2×C4×C31—22no—
479C2×C4×C31—22no—
480C2×C4×C31—22no—
481C2×C4×C31—22no—
482C2×C4×C31—22no—
483C2×C4×C31—22no—
484C2×C4×C31—22no—
485C2×C4×C31—22no—
486C2×C4×C31—22no—
487C2×C4×C31—22no—
488C2×C4×C31—22no—
489C2×C4×C31—22no—
490C2×C4×C31—22no—
491C2×C4×C31—22no—
492C2×C4×C31—22no—
493C2×C4×C31—22no—
494C2×C4×C31—22no—
495C2×C4×C31—22no—
496C2×C4×C31—416no—
497C2×C4×C31—41no—
498C2×C4×C31—41no—
499C2×C4×C31—41no—
500C2×C4×C31—41no—
501C2×C4×C31—41no—
502C2×C4×C31—41no—
503C2×C4×C31—41no—
504C2×C4×C31—41no—
505C2×C4×C31—41no—
506C2×C4×C31—41no—
507C2×C4×C31—41no—
508C2×C4×C31—41no—
509C2×C4×C31—41no—
510C2×C4×C31—41no—
511C2×C4×C31—41no—
512C2×C4×C31—41no—
513C2×C4×C31—41no—
514C2×C4×C31—41no—
515C2×C4×C31—41no—
516C2×C4×C31—41no—
517C2×C4×C31—41no—
518C2×C4×C31—41no—
519C2×C4×C31—41no—
520C2×C4×C31—41no—
521C2×C4×C31—41no—
522C2×C4×C31—41no—
523C2×C4×C31—41no—
524C2×C4×C31—41no—
525C2×C4×C31—41no—
526C2×C4×C31—41no—
527C2×C4×C31—41no—
528C2×C4×C31—41no—
529C2×C4×C31—41no—
530C2×C4×C31—41no—
531C2×C4×C31—41no—
532C2×C4×C31—41no—
533C2×C4×C31—41no—
534C2×C4×C31—41no—
535C2×C4×C31—41no—
536C2×C4×C31—41no—
537C2×C4×C31—41no—
538C2×C4×C31—41no—
539C2×C4×C31—41no—
540C2×C4×C31—41no—
541C2×C4×C31—41no—
542C2×C4×C31—41no—
543C2×C4×C31—41no—
544C2×C4×C31—41no—
545C2×C4×C31—41no—
546C2×C4×C31—41no—
547C2×C4×C31C4×D414yes—
548C2×#392C2×C3111yescharacteristic
549C2×#390C2×C3111yescharacteristic, complemented
550C2×#388C2×C3111yescharacteristic, complemented
551C2×#386C2×C3111yescharacteristic, complemented
552C2×#386C2×C3111yescharacteristic, complemented
553#1442C2×C3111yescharacteristic, complemented
554#1440C2×C3111yescharacteristic, complemented
555#1438C2×C3111yescharacteristic, complemented
556#1438C2×C3111yescharacteristic, complemented
557#1438C2×C3111yescharacteristic, complemented
558#1437C2×C3111yescharacteristic, complemented
559#1437C2×C3111yescharacteristic, complemented
560#1437C2×C3111yescharacteristic, complemented
561#1434C2×C3111yescharacteristic, complemented
562C22⋊#95C2×C3111yescharacteristic, complemented
563C22×C31—24no—
564C22×C31—24no—
565C22×C31—24no—
566C22×C31—42no—
567C22×C31—42no—
568C22×C31—42no—
569C22×C31—42no—
570C22×C31—42no—
571C22×C31—42no—
572C22×C31—42no—
573C22×C31—42no—
574C22×C31—42no—
575C22×C31—42no—
576C22×C31—42no—
577C22×C31—42no—
578C22×C31—42no—
579C22×C31—42no—
580C22×C31—42no—
581C22×C31—42no—
582C22×C31—42no—
583C22×C31—42no—
584C22×C31—42no—
585C22×C31—42no—
586C22×C31—42no—
587C22×C31—42no—
588C22×C31—42no—
589C22×C31—42no—
590C22×C31—42no—
591C22×C31—42no—
592C22×C31—81no—
593C22×C31—81no—
594C22×C31—81no—
595C22×C31—81no—
596C22×C31—81no—
597C22×C31—81no—
598C22×C31—81no—
599C22×C31—81no—
600C22×C31—81no—
601C22×C31—81no—
602C22×C31—81no—
603C22×C31—81no—
604C22×C31—81no—
605C22×C31—81no—
606C22×C31—81no—
607C22×C31—81no—
608C22×C31C2×C4×D411yescharacteristic
609C22×C31C2×C4×D411yescharacteristic
610C22×C31C4×#4111yescharacteristic
611C22×C31#51811yescharacteristic
612C22×C31#51811yescharacteristic
613C22×C31#51811yescharacteristic
614C22×C31#51811yescharacteristic
615C22×C31#53411yescharacteristic
616C22×C31#53511yescharacteristic
617C22×C31#53511yescharacteristic
618C22×C31#53511yescharacteristic
619C22×C31#53811yescharacteristic
620C22×C31#53811yescharacteristic
621C22×C31#53811yescharacteristic
622C22×C31#53811yescharacteristic
623C22×C31#54011yescharacteristic
624C22×C31#54011yescharacteristic
625C22×C31#54011yescharacteristic
626C22×C31#54011yescharacteristic
627C22×C31D4211yescharacteristic
628C22×C31#54611yescharacteristic
629C22×C31#54611yescharacteristic
630C22×C31#54611yescharacteristic
631C22×C31#54611yescharacteristic
632C22×C31#54611yescharacteristic
633C22×C31#55011yescharacteristic
634C22×C31#55111yescharacteristic
635C22×C31#55311yescharacteristic
636C22×C31#55311yescharacteristic
637C22×C31#55311yescharacteristic
638C22×C31#55511yescharacteristic
639C22×C31#56011yescharacteristic
640C22×C31#56011yescharacteristic
641C22×C31#56011yescharacteristic
642C22×C31H(3,𝔽4)11yescharacteristic
643C4×C31—24no—
644C4×C31—42no—
645C4×C31—42no—
646C4×C31—42no—
647C4×C31—42no—
648C4×C31—42no—
649C4×C31—42no—
650C4×C31—42no—
651C4×C31—42no—
652C4×C31—42no—
653C4×C31—81no—
654C4×C31—81no—
655C23×D4C22×C3111yescharacteristic
656C23×D4C22×C3111yescharacteristic
657C23×D4C22×C3111yescharacteristic
658C24×C4C22×C3111yescharacteristic
659C22×C4⋊C4C22×C3111yescharacteristic
660C22×C22⋊C4C22×C3111yescharacteristic
661C22×C22⋊C4C22×C3111yescharacteristic
662C22×C22⋊C4C22×C3111yescharacteristic
663C22×C22⋊C4C22×C3111yescharacteristic
664C22×C22⋊C4C22×C3111yescharacteristic
665C22×C22⋊C4C22×C3111yescharacteristic
666C22×C22⋊C4C22×C3111yescharacteristic
667C22×C22⋊C4C22×C3111yescharacteristic
668C22×C22⋊C4C22×C3111yescharacteristic
669C22×C22⋊C4C22×C3111yescharacteristic
670C22×C22⋊C4C22×C3111yescharacteristic
671C22×C22⋊C4C22×C3111yescharacteristic
672C22×C22⋊C4C22×C3111yescharacteristic
673C22×C22⋊C4C22×C3111yescharacteristic
674C22×C42C22×C3111yescharacteristic
675C22×C42C22×C3111yescharacteristic
676#392C4×C3118yescomplemented
677#390—24no—
678#388—24no—
679#386—24no—
680#386—24no—
681C2×#95C22×C3111yescharacteristic
682C2×#95C22×C3111yescharacteristic
683C2×#95C22×C3111yescharacteristic
684C2×#95C22×C3111yescharacteristic
685C2×#95C22×C3111yescharacteristic
686C2×#95C22×C3111yescharacteristic
687C2×#95C22×C3111yescharacteristic
688C2×#95C22×C3111yescharacteristic
689C2×#95C22×C3111yescharacteristic
690C2×#95C22×C3111yescharacteristic
691C2×#95C22×C3111yescharacteristic
692C2×#95C22×C3111yescharacteristic
693C2×#95C22×C3111yescharacteristic
694C2×#95C22×C3111yescharacteristic
695C2×C31—44no—
696C2×C31—82no—
697C2×C31—82no—
698C2×C31#232111yescharacteristic
699C2×C31#232811yescharacteristic
700C2×C31#233311yescharacteristic
701C2×C31#235811yescharacteristic
702C2×C31#236311yescharacteristic
703C2×C31#236411yescharacteristic
704C2×C31#237511yescharacteristic
705C2×C31#267011yescharacteristic
706C2×C31#267311yescharacteristic
707C2×C31#269911yescharacteristic
708C2×C31#270311yescharacteristic
709C2×C31#270311yescharacteristic
710C2×C31#271411yescharacteristic
711C2×C31#275311yescharacteristic
712C2×C31#275611yescharacteristic
713C25C23×C3111yescharacteristic
714C25C23×C3111yescharacteristic
715C25C23×C3111yescharacteristic
716C22×D4—22no—
717C22×D4—22no—
718C22×D4—22no—
719C22×D4—22no—
720C22×D4—22no—
721C22×D4—22no—
722C22×D4—41no—
723C22×D4—41no—
724C22×D4—41no—
725C22×D4—41no—
726C22×D4—41no—
727C22×D4—41no—
728C22×D4—41no—
729C22×D4—41no—
730C22×D4—41no—
731C22×D4—41no—
732C22×D4—41no—
733C22×D4—41no—
734C22×D4C2×C4×C3114yes—
735C22×D4C2×C4×C3114yes—
736C22×D4C2×C4×C3114yescomplemented
737C23×C4—22no—
738C23×C4—22no—
739C23×C4—22no—
740C23×C4—41no—
741C23×C4—41no—
742C23×C4—41no—
743C23×C4—41no—
744C23×C4C23×C3111yescharacteristic
745C23×C4C23×C3111yescharacteristic
746C23×C4C23×C3111yescharacteristic
747C23×C4C23×C3111yescharacteristic
748C23×C4C23×C3111yescharacteristic
749C23×C4C23×C3111yescharacteristic
750C23×C4C23×C3111yescharacteristic
751C23×C4C23×C3111yescharacteristic
752C23×C4C23×C3111yescharacteristic
753C23×C4C23×C3111yescharacteristic
754C23×C4C23×C3111yescharacteristic
755C23×C4C23×C3111yescharacteristic
756C2×C4⋊C4—22no—
757C2×C4⋊C4—22no—
758C2×C4⋊C4—41no—
759C2×C22⋊C4—22no—
760C2×C22⋊C4—22no—
761C2×C22⋊C4—22no—
762C2×C22⋊C4—22no—
763C2×C22⋊C4—22no—
764C2×C22⋊C4—22no—
765C2×C22⋊C4—22no—
766C2×C22⋊C4—22no—
767C2×C22⋊C4—22no—
768C2×C22⋊C4—22no—
769C2×C22⋊C4—22no—
770C2×C22⋊C4—22no—
771C2×C22⋊C4—22no—
772C2×C22⋊C4—22no—
773C2×C22⋊C4—22no—
774C2×C22⋊C4—22no—
775C2×C22⋊C4—22no—
776C2×C22⋊C4—22no—
777C2×C22⋊C4—41no—
778C2×C22⋊C4—41no—
779C2×C22⋊C4—41no—
780C2×C22⋊C4—41no—
781C2×C22⋊C4—41no—
782C2×C22⋊C4—41no—
783C2×C22⋊C4—41no—
784C2×C22⋊C4—41no—
785C2×C22⋊C4—41no—
786C2×C22⋊C4—41no—
787C2×C22⋊C4—41no—
788C2×C22⋊C4—41no—
789C2×C22⋊C4—41no—
790C2×C22⋊C4—41no—
791C2×C22⋊C4—41no—
792C2×C22⋊C4—41no—
793C2×C22⋊C4—41no—
794C2×C22⋊C4—41no—
795C2×C22⋊C4—41no—
796C2×C22⋊C4—41no—
797C2×C22⋊C4C2×C4×C3114yes—
798C2×C22⋊C4C2×C4×C3114yescomplemented
799C2×C22⋊C4C2×C4×C3114yescomplemented
800C2×C22⋊C4D4×C3114yescomplemented
801C2×C42—22no—
802C2×C42—22no—
803C2×C42—22no—
804C2×C42—41no—
805C2×C42—41no—
806C2×C42—41no—
807#95—22no—
808#95—22no—
809#95—22no—
810#95—22no—
811#95—41no—
812#95—41no—
813#95—41no—
814#95—41no—
815#95—41no—
816#95—41no—
817#95—41no—
818#95—41no—
819#95C2×C4×C3114yescomplemented
820#95D4×C3114yescomplemented
821C31#1452011yescharacteristic, direct product factor, Sylow
822C24—21no—
823C24—21no—
824C24—21no—
825C24—21no—
826C24—21no—
827C24—21no—
828C24—21no—
829C24—21no—
830C24—21no—
831C24—21no—
832C24—21no—
833C24—21no—
834C24—21no—
835C24—21no—
836C24—21no—
837C24—21no—
838C24—21no—
839C24—21no—
840C24—21no—
841C24—21no—
842C24—21no—
843C24—21no—
844C24—21no—
845C24—21no—
846C24—21no—
847C24—21no—
848C24—21no—
849C24—21no—
850C24—21no—
851C24—21no—
852C24—21no—
853C24—21no—
854C24—21no—
855C24—21no—
856C24—21no—
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24—21no—
862C24C22×C4×C3112yes—
863C24C22×C4×C3112yes—
864C24C22×C4×C3112yes—
865C24C2×D4×C3112yes—
866C24#41×C3112yes—
867C24C24×C3111yescharacteristic
868C2×D4—28no—
869C2×D4—28no—
870C2×D4—28no—
871C2×D4—44no—
872C2×D4—44no—
873C2×D4—44no—
874C2×D4—44no—
875C2×D4—44no—
876C2×D4—44no—
877C2×D4—44no—
878C2×D4—44no—
879C2×D4—44no—
880C2×D4—44no—
881C2×D4—44no—
882C2×D4—44no—
883C2×D4—44no—
884C2×D4—44no—
885C2×D4—44no—
886C2×D4—44no—
887C2×D4—44no—
888C2×D4—44no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—44no—
962C22×C4—44no—
963C22×C4—44no—
964C22×C4—44no—
965C22×C4—44no—
966C22×C4—44no—
967C22×C4—44no—
968C22×C4C22×C4×C3112yes—
969C22×C4C22×C4×C3112yes—
970C22×C4C22×C4×C3112yes—
971C22×C4C22×C4×C3112yes—
972C22×C4C2×D4×C3112yes—
973C22×C4C2×D4×C3112yes—
974C22×C4C2×D4×C3112yes—
975C22×C4C2×D4×C3112yes—
976C22×C4C2×D4×C3112yes—
977C22×C4#41×C3112yes—
978C22×C4#41×C3112yes—
979C22×C4#41×C3112yes—
980C4⋊C4—44no—
981C22⋊C4—28no—
982C22⋊C4—44no—
983C22⋊C4—44no—
984C22⋊C4—44no—
985C22⋊C4—44no—
986C22⋊C4—44no—
987C22⋊C4—44no—
988C22⋊C4—44no—
989C22⋊C4—44no—
990C22⋊C4—44no—
991C22⋊C4—44no—
992C22⋊C4—44no—
993C22⋊C4—44no—
994C22⋊C4—44no—
995C42—44no—
996C42—44no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—22no—
1012C23—22no—
1013C23—22no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23C4×D4×C3114yes—
1102C23C23×C4×C3111yescharacteristic
1103C23C22×D4×C3111yescharacteristic
1104C23C22×D4×C3111yescharacteristic
1105C23C2×#41×C3111yescharacteristic
1106C23C2×#41×C3111yescharacteristic
1107C23C2×#41×C3111yescharacteristic
1108C23C2×#41×C3111yescharacteristic
1109C23C31×H(5,𝔽2)11yescharacteristic
1110C23C31×H(5,𝔽2)11yescharacteristic
1111C23C31×H(5,𝔽2)11yescharacteristic
1112C23C31×H(5,𝔽2)11yescharacteristic
1113C23C31×H(5,𝔽2)11yescharacteristic
1114C23C31×H(5,𝔽2)11yescharacteristic
1115C23C31×H(5,𝔽2)11yescharacteristic
1116C23C31×H(5,𝔽2)11yescharacteristic
1117D4—416no—
1118D4—416no—
1119D4—416no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—416no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4C4×D4×C3114yes—
1205C22—24no—
1206C22—24no—
1207C22—24no—
1208C22—42no—
1209C22—42no—
1210C22—42no—
1211C22—42no—
1212C22—42no—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—42no—
1219C22—42no—
1220C22—42no—
1221C22—42no—
1222C22—42no—
1223C22—42no—
1224C22—42no—
1225C22—42no—
1226C22—42no—
1227C22—42no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—81no—
1235C22—81no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22—81no—
1243C22—81no—
1244C22—81no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22C2×C4×D4×C3111yescharacteristic
1251C22C2×C4×D4×C3111yescharacteristic
1252C22C4×#41×C3111yescharacteristic
1253C22C31×#51811yescharacteristic
1254C22C31×#51811yescharacteristic
1255C22C31×#51811yescharacteristic
1256C22C31×#51811yescharacteristic
1257C22C31×#53411yescharacteristic
1258C22C31×#53511yescharacteristic
1259C22C31×#53511yescharacteristic
1260C22C31×#53511yescharacteristic
1261C22C31×#53811yescharacteristic
1262C22C31×#53811yescharacteristic
1263C22C31×#53811yescharacteristic
1264C22C31×#53811yescharacteristic
1265C22C31×#54011yescharacteristic
1266C22C31×#54011yescharacteristic
1267C22C31×#54011yescharacteristic
1268C22C31×#54011yescharacteristic
1269C22D42×C3111yescharacteristic
1270C22C31×#54611yescharacteristic
1271C22C31×#54611yescharacteristic
1272C22C31×#54611yescharacteristic
1273C22C31×#54611yescharacteristic
1274C22C31×#54611yescharacteristic
1275C22C31×#55011yescharacteristic
1276C22C31×#55111yescharacteristic
1277C22C31×#55311yescharacteristic
1278C22C31×#55311yescharacteristic
1279C22C31×#55311yescharacteristic
1280C22C31×#55511yescharacteristic
1281C22C31×#56011yescharacteristic
1282C22C31×#56011yescharacteristic
1283C22C31×#56011yescharacteristic
1284C22C31×H(3,𝔽4)11yescharacteristic
1285C4—24no—
1286C4—42no—
1287C4—42no—
1288C4—42no—
1289C4—42no—
1290C4—42no—
1291C4—42no—
1292C4—42no—
1293C4—42no—
1294C4—42no—
1295C4—81no—
1296C4—81no—
1297C2—44no—
1298C2—82no—
1299C2—82no—
1300C2C31×#232111yescharacteristic
1301C2C31×#232811yescharacteristic
1302C2C31×#233311yescharacteristic
1303C2C31×#235811yescharacteristic
1304C2C31×#236311yescharacteristic
1305C2C31×#236411yescharacteristic
1306C2C31×#237511yescharacteristic
1307C2C31×#267011yescharacteristic
1308C2C31×#267311yescharacteristic
1309C2C31×#269911yescharacteristic
1310C2C31×#270311yescharacteristic
1311C2C31×#270311yescharacteristic
1312C2C31×#271411yescharacteristic
1313C2C31×#275311yescharacteristic
1314C2C31×#275611yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutatorC23C23×C4×C31
Frattini, cosocleC24C24×C31
prime radicalC2×C31×#392C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×C31×#390C2semidirect
3. C2×C31×#388C2semidirect
4. C2×C31×#386C2semidirect
5. C2×C31×#386C2semidirect
6. C31×#1442C2semidirect
7. C31×#1440C2semidirect
8. C31×#1438C2semidirect
9. C31×#1438C2semidirect
10. C31×#1438C2semidirect
11. C31×#1437C2semidirect
12. C31×#1437C2semidirect
13. C31×#1437C2semidirect
14. C31×#1434C2semidirect
15. C31×C22⋊#95C2semidirect
37. C31×#392C4semidirect
79. C22×D4×C31C2×C4semidirect
141. C2×C22⋊C4×C31C2×C4semidirect
142. C2×C22⋊C4×C31C2×C4semidirect
143. C2×C22⋊C4×C31D4semidirect
162. C31×#95C2×C4semidirect
163. C31×#95D4semidirect
339. #14520C31direct (N × H)
549. C2×#390C2×C31semidirect
550. C2×#388C2×C31semidirect
551. C2×#386C2×C31semidirect
552. C2×#386C2×C31semidirect
553. #1442C2×C31semidirect
554. #1440C2×C31semidirect
555. #1438C2×C31semidirect
556. #1438C2×C31semidirect
557. #1438C2×C31semidirect
558. #1437C2×C31semidirect
559. #1437C2×C31semidirect
560. #1437C2×C31semidirect
561. #1434C2×C31semidirect
562. C22⋊#95C2×C31semidirect
676. #392C4×C31semidirect
736. C22×D4C2×C4×C31semidirect
798. C2×C22⋊C4C2×C4×C31semidirect
799. C2×C22⋊C4C2×C4×C31semidirect
800. C2×C22⋊C4D4×C31semidirect
819. #95C2×C4×C31semidirect
820. #95D4×C31semidirect
821. C31#14520direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C31×#3922
C2×C31×#3902
C2×C31×#3882
C2×C31×#3862
C31×#14422
C31×#14402
C31×#14382
C31×#14372
C31×#14342
C31×C22⋊#952
#1452031